加性DEA模型与规模收益

[1]给出了用C^2R模型或C^2GS^2模型来判断决策单元的规模收益情况的定理,指出它有时失效。对DEA有效（C^2GS^2）的决策单元,本用加性DEA模型来有效地判断其规模收益情况。     

Chapter 11 Simulation studies of efficiency,returns to scale and misspecification with nonlinear functions in DEA

Using statistically designed experiments, 12,500 observations are generated from a 4-pieced Cobb-Douglas function exhibiting increasing and decreasing returns to scale in its different pieces. Performances of DEA and frontier regressions represented by COLS (Corrected Ordinary Least Squares) are compared at sample sizes ofn=50, 100, 150 and 200. Statistical consistency is exhibited, with performances improving as sample sizes increase. Both DEA and COLS generally give good results at all sample sizes. In evaluating efficiency, DEA generally shows superior performance, with BCC models being best (except at corner points), followed by the CCR model and then by COLS, with log-linear regressions performing better than their translog counterparts at almost all sample sizes. Because of the need to consider locally varying behavior, only the CCR and translog models are used for returns to scale, with CCR being the better performer. An additional set of 7,500 observations were generated under conditions that made it possible to compare efficiency evaluations in the presence of collinearity and with model misspecification in the form of added and omitted variables. Results were similar to the larger experiment: the BCC model is the best performer. However, COLS exhibited surprisingly good performances — which suggests that COLS may have previously unidentified robustness properties — while the CCR model is the poorest performer when one of the variables used to generate the observations is omitted.     

A new robust mixed integer-valued model in DEA

The mixed integer linear programming (MILP) models are proposed to estimate the performance of decision making units (DMUs) including both integer and real values in data envelopment analysis (DEA). There are several studies to propose MILPs in the literature of DEA; however, they have some major shortcomings unfortunately. This study firstly mentioned the shortcomings in the previous researches and secondly suggests a robust MILP based on the Kourosh and Arash Method (KAM). The proposed linear model, integer-KAM (IKAM), has almost all capabilities of the linear KAM and significantly removes the shortcomings in the current MILPs. For instance, IKAM benchmarks and ranks all technically efficient and inefficient DMUs at the same time. It detects outliers, and estimates the production frontier significantly. A numerical example of 39 Spanish airports with four integer inputs and three outputs including two integer values and a real value also represents the validity of the statements.     

Decomposing technical efficiency and scale elasticity in two-stage network DEA

The constant returns to scale assumption maintained by neoclassical theorists for justifying the black-box structure of production technology in long run does not necessarily allow one to infer that there are no scale benefits available in its sub-technologies. Most of real-life production technologies are multi-stage in nature, and the sources of increasing returns lie in the sub-technologies. It is, therefore, imperative to estimate the scale economies of a firm not only for the network technology but also for the sub-technologies. To accomplish this, two approaches are suggested in this contribution, based on the premise concerning whether a network technology construct considers allocative inefficiency. The first approach, which is ours, makes use of a single network technology for two interdependent sub-technologies. The second approach, which is due to Kao and Hwang (2011), however, assumes complete allocative efficiency by considering two independent sub-technology frontiers, one for each sub-technology. The distinction between these two approaches is important from a policy point of view since the network efficiencies revealed from these two approaches have distinctive causative factors that do not permit them to be used interchangeably.     

A dual simplex-based method for determination of the right and left returns to scale in DEA

This study reviews the concept of the “right” and the “left” returns to scale (RTS) in data envelopment analysis (DEA), and a dual simplex-based method, for determining these two notions in RTS, is proposed, which has computational advantages as compared to the customary method.     

An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties

This study discusses nine desirable properties that a measure of technical efficiency (TE) needs to satisfy from the perspective of production economics and optimization. Seven data envelopment analysis (DEA) models are theoretically compared from a viewpoint of nine TE criteria. All the seven DEA models suffer from a problem of multiple projections even though a unique projection for efficiency comparison is one of the nine desirable properties. Furthermore, all the DEA models violate the property on aggregation of inputs and outputs. Thus, the seven DEA models do not satisfy all desirable TE properties. In addition, the comparison provides us with the following guidelines: (a) The additive model violates all desirable TE properties. (b) Russell measure and SBM (=ERGM) perform as well as RAM as a non-radial measure. If we are interested in strict monotonicity, the two models outperform the other DEA models including RAM. In contrast, if we are interested in translation invariance, RAM is better than Russell measure and SBM (=ERGM). (c) The radial measures (CCR and BCC) have the property of linear homogeneity. (d) The CCR model is useful for measuring a frontier shift among different periods. (e) If a data set contains a negative value, RAM becomes a DEA model to handle the negative value because it has the property of translation invariance. After examining the desirable TE properties, this study proposes a new approach to deal with an occurrence of multiple projections. The proposed approach includes a test to examine an occurrence of multiple projections, a mathematical expression of a projection set, and a selection process of a unique reference set as the largest one covering all the possible reference sets.     

Preface to topics in data envelopment analysis

This paper serves as an introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of window analyses' to study DEA efficiency measures with an illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating, sources of inefficiency by means of artificially generated data, and (3) an extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested.This research was partly supported by the National Science Foundation and USARI Contract MDA 903-83-K0312, with the Center for Cybernetic Studies, the University of Texas at Austin. It was also partly supported by the IC² Institute at the University of Texas at Austin. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

Dynamic concept of returns to scales and its characteristics on production frontier in intersection form

This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale(RTS) of economic units with multiple inputs and outputs.It is frequently noticed that when we increase the input of a decision making unit(DMU) with a certain status of RTS,different status of RTS is observed.For example,when we increase the input of a DMU with constant RTS under the traditional method,a decreasing RTS is often observed instead of the expected constant RTS.We thus define the RTS of each DMU in both input expansion and contraction regions respectively.The research starts from transferring the production possibility set into the intersection form,by giving the explicit linear inequality representation of production frontiers.The RTS structural characteristics of DMUs’ on the production frontier are described.Status of RTS of those DMUs on the production frontier include increasing RTS,constant RTS,decreasing RTS,saturated RTS and evidence of congestion.Necessary and suficient conditions for RTS evaluation are provided.The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.     

Finding the efficiency score and RTS characteristic of DMUs by means of identifying the efficient frontier in DEA

Data envelopment analysis (DEA) is basically a linear programming based technique used for measuring the relative performance of organizational units, referred to as decision-making units (DMUs), where the presence of multiple inputs and outputs makes comparisons difficult. The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, a method for identifying the efficient frontier is introduced. Then, the efficiency score and returns to scale (RTS) characteristic of DMUs will be produced by means of the equation of efficient frontier.     

On the existence and computation of an equilibrium in an economy with constant returns to scale production

In this paper we consider the problem of finding an equilibrium in an economy with non-linear constant returns to scale production activities. To find an equilibrium we propose an adjustment process in which the prices of the commodities and the activity levels of production adjust simultaneously. The process starts at a price vector at which each production activity has non-positive profit. We show that the process follows a path which connects the starting point with an equilibrium of the economy. From this it follows that the existence of a price vector at which each production activity has non-positive profit implies the existence of an equilibrium. The equilibrium can be computed by using a simplicial algorithm or by solving a sequence of Linear Variational Inequality Problems.This research is part of the VF-program Competition and Cooperation. The authors are very grateful to Dolf Talman and two unknown referees for their valuable comments and suggestions.     

Measurement of simultaneous scale and mix changes in inputs and outputs using DEA facets and RTS

We show a new use of the efficient facets in DEA. Specifically, once we have identified all facets of the DEA technology, we are able to estimate the potential changes in some inputs and outputs, while fixing other inputs and outputs, ranges of simultaneous scale and mix changes in inputs and outputs, while proportionally increasing or decreasing other inputs and outputs, and, finally, the RTS. The proposed algorithms are applied to corporate planning processes of chemical companies.     

Evaluating returns to scale and congestion by production possibility set in intersection form

This research proposes a new method to estimate returns to scale(RTS) of decision making units(DM Us) with multiple inputs and outputs.The state of return to scale includes increasing RTS,constant RTS,decreasing RTS and evidence of congestion.The method is based on the production possibility set in the intersection form given by a set of linear inequalities.We propose and prove the necessary and sufficient conditions for the RTS estimation.With the new procedure,to estimate the RTS of a DM U is simply to ch...     

Combining the assumptions of variable and constant returns to scale in the efficiency evaluation of secondary schools

Our paper reports on the use of data envelopment analysis (DEA) for the assessment of performance of secondary schools in Malaysia during the implementation of the policy of teaching and learning mathematics and science subjects in the English language (PPSMI). The novelty of our application is that it makes use of the hybrid returns-to-scale (HRS) DEA model. This combines the assumption of constant returns to scale with respect to quantity inputs and outputs (teaching provision and students) and variable returns to scale (VRS) with respect to quality factors (attainment levels on entry and exit) and socio-economic status of student families. We argue that the HRS model is a better-informed model than the conventional VRS model in the described application. Because the HRS technology is larger than the VRS technology, the new model provides a tangibly better discrimination on efficiency than could be obtained by the VRS model. To assess the productivity change of secondary schools over the years surrounding the introduction of the PPSMI policy, we adapt the Malmquist productivity index and its decomposition to the case of HRS model.     

Properties of the sequential gradient-restoration algorithm (SGRA), part 1: Introduction and comparison with related methods

The sequential gradient-restoration algorithm (SGRA) was developed in the late 1960s for the solution of equality-constrained nonlinear programs and has been successfully implemented by Miele and coworkers on many large-scale problems. The algorithm consists of two major sequentially applied phases. The first is a gradient-type minimization in a subspace tangent to the constraint surface, and the second is a feasibility restoration procedure. In Part 1, the original SGRA algorithm is described and is compared with two other related methods: the gradient projection and the generalized reduced gradient methods. Next, the special case of linear equalities is analyzed. It is shown that, in this case, only the gradient-type minimization phase is needed, and the SGRA becomes identical to the steepest-descent method. Convergence proofs for the nonlinearly constrained case are given in Part 2.Partial support for this work was provided by the Fund for the Promotion of Research at Technion, Israel Institute of Technology, Haifa, Israel.     

虚拟企业管理中的伙伴选择问题:模型与理论分析

本文建立了虚拟企业伙伴选择问题的整数规划模型，并从理论上证明了该类问题正规解的存在性．所获结果对于该类问题的研究与求解提供了可靠的理论依据，并将建立的模型和所得结论应用到一个工程实际问题，采用遗传算法求解，取得了满意的计算结果．     

Informal Networks and Resistance to Organizational Change: The Introduction of Quality Standards in a Transport Company

In this paper we investigate the association between resistance to the introduction of ISO quality standards in a transport company and three effects of the informal advice and trust networks in the organization. The analysis includes four prevailing explanations from the literature on organizational resistance: job satisfaction, perceived legitimacy, unit grouping and decision making authority. The network effects we propose are: (a) a contagion effect, which predicts that members with the same opinion tend to have close or equal trust and advice relations; (b) a prominence effect, which predicts that prominent actors in the trust network show less resistance than other members—and that prominent members of the advice network show more resistance than less prominent actors; (c) a role equivalence effect, which predicts that members with the same patterns of combined trust/advice relations show the same resistance. The paper presents the operationalization and measurement of the variables and the results of three analyses to test the effects. Contagion of resistance appears to be very significant in the trust network. Resistance gradually erodes in the trust network when moving from management to employees. Members who are trusted in the transport company are significantly less resistant to the introduction of the quality standards than members who are not especially trusted. This network effect is controlled for the significant effects of job satisfaction and perceived legitimacy. The role equivalence structure of the combined trust/advice network does not explain the resistance. We conclude that informal networks have important effects on resistance to the proposed changes in the transport company. The case study shows how network analysis can be used to empirically test for effects of social relations in organizations.     

Fejér processes in theory and practice: Recent results

In this paper we briefly survey the recent results of the theory of Fejér mappings and processes as applied to solving various mathematical problems, including structured systems of linear and convex inequalities, operator equations, as well as problems of linear and quadratic programming which are not necessarily solvable (improper ones).     

Parking Capacity and Pricing in Park'n Ride Trips: A Continuous Equilibrium Network Design Problem

In this paper we consider the problem of designing parking facilities for park'n ride trips. We present a new continuous equilibrium network design problem to decide the capacity and fare of these parking lots at a tactical level. We assume that the parking facilities have already been located and other topological decisions have already been taken.The modeling approach proposed is mathematical programming with equilibrium constraints. In the outer optimization problem, a central Authority evaluates the performance of the transport network for each network design decision. In the inner problem a multimodal traffic assignment with combined modes, formulated as a variational inequality problem, generates the share demand for modes of transportation, and for parking facilities as a function of the design variables of the parking lots. The objective is to make optimal parking investment and pricing decisions in order to minimize the total travel cost in a subnetwork of the multimodal transportation system.We present a new development in model formulation based on the use of generalized parking link cost as a design variable.The bilevel model is solved by a simulated annealing algorithm applied to the continuous and non-negative design decision variables. Numerical tests are reported in order to illustrate the use of the model, and the ability of the approach to solve applications of moderate size.